Intrapore convection when the average temperature gradient is vertical

Abstract

The heat conduction of a porous medium saturated with a fluid is usually regarded as being purely molecular [1]. The assumption here is that in the case of heating from below the local temperature gradient within each of the pores, like the averaged gradient in the complete layer, is strictly vertical, and, since the pores are as a rule small, this local gradient is less than the critical. It is therefore assumed that in the absence of large-scale convection the fluid in the pores is in equilibrium. However, for different thermal conductivities of the fluid and the porous skeleton surrounding it a vertical temperature gradient in the fluid and, accordingly, equilibrium of the fluid are possible only if a cavity is a sphere or an ellipsoid with a definite orientation [1]. Since the pores do not have such shapes, the convective motion that arises in each of the pores or in several communicating pores can lead to an increase in the effective thermal conductivity of the fluid and, accordingly, the effective thermal conductivity of the complete medium. The present paper is devoted to study of this effect.